Light and Mirrors Part II MIRRORS 1

Polarized Sunglasses- How do they work? light waves vibrate in more than one plane light waves can be made to vibrate in a single plane by use of polarizing filters. 2

polarizing magic 3

Speed of Light The speed of all EM Waves (light) or “c” is 3 x 10 8 m/s. What is a light year? The distance light travels in one year Does light ever go slower? Yes, 3 x 10 8 m/s is the maximum and occurs in an vacuum. When it enters a medium, it slows down.

Light at a Boundary Absorbed (“Stuck inside”) Pass through the boundary (transmitted) –Medium Changes –Therefore Speed Changes –What is this called? –Refraction Bounce off the boundary –Medium its traveling through does not change –Therefore Speed remains same –What is this called? –Reflection 5

Reflection and Refraction at an Interface Why does the light bend?

7 Reflection and Mirrors

REFLECTION OF LIGHT Light obeys the law of refection that states that: "The angle of incidence is equal to the angle of reflection."

Angle of Reflection = Angle of Incidence Angles are measured with respect to the normal line

If all surfaces reflect, why can’t I see my image?

Light reflection from a smooth surface is called regular or specular reflection. Light reflection from a rough or irregular surface is called diffuse reflection.

What type of reflection?

Fiber Optics is also an example of reflection TOTAL INTERNAL REFLECTION

Total Internal Reflection!!!

Mirrors

When we look at something in the mirror, the light wave we see is the reflected ray:

19 Object: source of rays Image: reproduction of object

20 Describing Images Size –Same –Reduced –Enlarged Orientation –Upright or inverted, Reversed Virtual or Real

21 Virtual reflected rays do not actually converge to form image. Cannot be projected. images form where light rays appear to have crossed. In mirrors, they form behind the mirror. are always upright.

22 Real images form where light rays actually cross. Can be projected. In mirrors, they form on the same side of the mirror as the object since light can not pass through a mirror. are always inverted (flipped upside down).

23 Types of Mirrors Flat or Plane Concave (Converging) Convex (Diverging)

FLAT MIRRORS Object Location: NA Virtual Erect Same Size Behind

FLAT MIRRORS A flat mirror reflects light rays in the same order as they approach it. Flat mirrors are made from pieces of plate glass that have been coated on the back with a reflecting material like silver or aluminum. The image is the same size as the object and the same distance behind the mirror as the object is in front of the mirror.

These images which appear to the eye to be formed by rays of light but which in truth do not exist are called virtual images. On the other hand real images are formed when rays of light actually intersect at a single point. Notice that the images formed by a flat mirror are, in truth, reflections of real objects. The images themselves are not real because no light passes through them.

27 Think about your image in a plane mirror? What is the same? What is different?

28 Images in a plane mirror are also reversed left to right.

Mirrors actually reverse you front to back, it is like turning a glove inside out

30 Plane Mirror In a plane mirror the object is the same size, upright, and the same distance behind the mirror as the object is in front of the mirror. Your mind extends the reflected ray beyond the mirror to form image.

31 Types of Mirrors Concave Concave Mirrors Object Location: Near Object Location: Far Virtual Real Erect Inverted Enlarged Reduced Behind In Front Concave mirrors: sphere whose inner surface was reflective aka converging mirrors since they bring light rays to a focus. ex. magnifying mirrors

32 Convex Convex Mirrors Object Location: NA Virtual Erect Reduced Behind Convex mirrors: sphere whose outer surface was reflective. aka diverging mirrors since spread out light rays. ex store security mirrors

Convex Mirrors

36 What kind of mirror would be used to focus a beam of light? Concave

37 Ray Diagrams F: Focal Point, point where parallel light rays converge or appear to diverge. The focal point (F) is located halfway between the mirror’s surface and the center of curvature. f: focal length, distance between F and mirror/lens C: Center of curvature, geometric center of sphere of radius. C = 2f =radius Principle axis: line that passes through both the center of curvature (C) and the focal point (F) and intersects the mirror at a right angle.

38 FC Principle Axis Concave Mirrors Light source Convex Mirrors FC Principle Axis Light source

A curved mirror has a geometric center or vertex A The center of curvature or radius C The focal length f of the mirror is half the radius

40 C=2f f = ? C/2

41 A concave mirror has a radius of curvature of 15 cm. What is the focal length of this mirror? A. 15 cm B. 30 cm C. 7.5 cm

42

43 1. Start at top of object. Light ray 1 travels parallel to the principle axis, strikes the mirror, and is reflected back through the focal point (F). 2. Light ray 2 travels from top of object and strikes the mirror, is in line with the focal point. It is reflected back parallel to the principle axis. 3. Where these 2 reflected light rays intersect is the location of the image. Sometimes it is necessary to extend reflected rays beyond mirror. If above axis, erect; if below, inverted. Ray Diagram Rules

44 Hints Images in front of mirror are always real Real Images are always inverted Inverted images are always below the principle axis If reflected rays do not cross, extend them behind mirror Images behind mirror are always virtual Virtual Images are always erect Erect images are always above the principle axis

Perform Ray Diagram Use Table in notes to summarize 45

46 Object Location Real or Virtual Erect or Inverted Size Plane Mirror Concave Mirror Convex Mirror

47 Locating images in concave mirrors Fill in hypertextbook.com

48 Describe image when Object located beyond C Real or Virtual? Real Erect or Inverted? Inverted Same size, Enlarged or Reduced? Reduced Location? Between f and C Concave Mirror

49 Concave Mirror with the Object located beyond C

50 Light rays that travel parallel to the principle axis, strike the mirror, and are reflected back through the focal point (f). Concave Mirror Object beyond C

51 Light rays that travel through the focal point (f), strike the mirror, and are reflected back parallel to the principle axis. Concave Mirror Object beyond C

52 Concave Mirror Object beyond C Image: Real Inverted Smaller Between f and C The image is located where the reflected light rays intersect

53 Concave Mirror with the Object located at C

54 Concave Mirror Object at C Light rays that travel parallel to the principle axis, strike the mirror, and are reflected back through the focal point (f).

55 Concave Mirror Object at C Light rays that travel through the focal point (f), strike the mirror, and are reflected back parallel to the principle axis.

56 Concave Mirror Object at C Image: Real Inverted Same Size At C The image is located where the reflected light rays intersect

57 Concave Mirror with the Object located between f and C

58 Describe image when Object located between f and C Real or Virtual? Real Erect or Inverted? Inverted Same size, Enlarged or Reduced? Larger Location? Beyond C Concave Mirror

59 Concave Mirror Object between f and C Light rays that travel parallel to the principle axis, strike the mirror, and are reflected back through the focal point (f). fC

60 Concave Mirror Object between f and C Light rays that travel through the focal point (f), strike the mirror, and are reflected back parallel to the principle axis. fC

61 Concave Mirror Object between f and C Image: Real Inverted Larger Beyond C The image is located where the reflected light rays intersect fC

62 Concave Mirror with the Object located at f

63 Concave Mirror Object at f Light rays that pass through the center of curvature hit the mirror and are reflected back along the same path.

64 Concave Mirror Object at f Light rays that travel parallel to the principle axis, strike the mirror, and are reflected back through the focal point (f).

65 Concave Mirror Object at f No image is formed. All reflected light rays are parallel and do not cross

66 Concave Mirror with the Object located between f and the mirror

67 Describe image when Object located between f and mirror Real or Virtual? Virtual Erect or Inverted? Erect Same size, Enlarged or Reduced? Larger Location? Further away, behind mirror Concave Mirror

68 Concave Mirror Object between f and the mirror Light rays that travel through the focal point (f), strike the mirror, and are reflected back parallel to the principle axis.

69 Light rays that travel parallel to the principle axis, strike the mirror, and are reflected back through the focal point (f). Concave Mirror Object between f and the mirror

70 Concave Mirror Object between f and the mirror Image: Virtual Upright Larger Further away The image is located where the reflected light rays intersect

71 Locating images in convex mirrors

72 Convex Mirror with the Object located anywhere in front of the mirror

73 Light rays that travel parallel to the principle axis, strike the mirror, and are reflected back through the focal point (f). f is negative. Convex Mirror Object located anywhere fC

74 Light rays that travel through (toward) the focal point (f), strike the mirror, and are reflected back parallel to the principle axis. Convex Mirror Object located anywhere fC

75 Convex Mirror Object located anywhere Image: Virtual Upright Smaller Behind mirror, inside f d i is negative The image is located where the reflected light rays intersect fC

Warm up #2 What part of the EM spectrum causes sunburn? Can it penetrate glass? 4/11 Friday we drew ray diagrams. If you were absent, you will have to complete these and show them to me. You will need a calculator today. Have notes out Houses Due Wed, Test on Friday

THE MIRROR EQUATION The mirror equation can be used to locate the image: The ratio M is called the magnification, h o is the object’s size and h i is the image size. Where d o is the object’s distance, d i is the image distance and f is the focal length.

78 F = focal point f =focal length = C/2 or r/2 C = center of curvature, radius d o = distance between object and mirror/lens d i = distance between image and mirror/lens h o = height of object h i = height of image m = optical enlargement of an object, ratio of size of image to size of object

R radius of curvature “C” + converging Concave Mirror - diverging Convex Mirror f focal length + converging- diverging dodo object distance + real object didi image distance + real images - virtual images hoho object size+ if upright hihi image size+ if upright- if inverted

80 Magnification + Upright Virtual - Inverted Real > 1 Enlarged < 1 Reduced

Ex 2 A concave mirror has a focal length of 25 cm. An object is placed 32 cm from the mirror. f = 25 cm d o = 32 cm 1/d i = 1/25cm – 1/32cm 1/d i = d i = cm 1di1di What kind of image? Why? Real, object beyond F in concave mirror Calculate d i 1do1do = 1f1f -

b. What is the magnification? f = 25 cm d o = 32 cm d i = cm M = Negative means upside down, enlarged if greater than one -d i d 0 = M = cm 32 cm

Ex 3 A smooth reflective disco ball hangs from a ceiling. It has a diameter of 50 cm. An object (16 cm tall) is placed 3 meters from the mirror. diameter = 50 cm What is C and f? Why is f negative? d o = 3 meters (is this unit a problem?) 1/d i = 1/-12.5cm -1/300cm 1/d i = d i = -12 cm Negative because behind mirror 1di1di What kind of image? Why? Virtual, all images are upright in convex mirror Calculate d i 1do1do = 1f1f - f= cm d o = 300 cm h o = 16 cm

Ex 3 A smooth reflective disco ball hangs from a ceiling. It has a diameter of 50 cm. An object (16 cm tall) is placed 3 meters from the mirror. diameter = 50 cm What is C and f? d o = 3 meters (is this unit a problem?) M = - -12cm/300cm M = 0.04 h i = 0.04 (16 cm) = 0.64cm M What is the height of the image? Determine M, then use that to determine image height Calculate M didodido = - f= cm d o = 300 cm h o = 16 cm d i = -12 cm

Example 4: Suppose you are 19 cm to the side of the bell of your friend’s trumpet and you see your image at 14 cm. Treating this as a concave mirror, what would be its focal length and radius of curvature? d o = 19 cm d i = 14 cm f = 8.06 cm R = 2f = 2(8.06cm) = cm 1 19cm = 1f1f 1 14cm +

A CHALLENGE Problem Example 5: Suppose you place a 5.0 cm tall pencil in front of a concave mirror. The mirror has a focal length of 24 cm. The pencil forms an image that appears to be at the same position as the pencil, but the image is inverted. a. Where did you place the pencil? h o = 5 cm f = 24 cm d o = d i d o = 2f = 2(24cm) = 48 cm So… 2do2do = 1f1f

b. How tall is the pencil’s image? h o = 5 cm h i = -h o = - 5 cm h i h 0 =